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Prime ideals and maximal ideals in semigroups. (English) Zbl 0176.29503


MSC:

20M12 Ideal theory for semigroups
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References:

[1] W. M. Faucett R. J. Koch, K. Numakura: Complements of maximal ideals in compact semigroups. Duke Math. J. 22 (1955), 655-661. · Zbl 0065.25303 · doi:10.1215/S0012-7094-55-02270-5
[2] L. Lesieur R. Croisot: Algèbre noethérienne non commutative. Mémorial des Sciences Mathématiques, Paris, 1963. · Zbl 0115.02903
[3] Jiang Luh: On the concept of radical of semigroups having kernel. Portugaliae Mathematica 19 (1960), 189-198. · Zbl 0095.01405
[4] R. J. Koch, A. D. Wallace: Maximal ideals in compact semigroups. Duke Math. J. 21 (1954), 681-685. · Zbl 0057.01502 · doi:10.1215/S0012-7094-54-02170-5
[5] K. Numakura: Prime ideals and idempotents in compact semigroups. Duke Math. J. 24 (1957), 671-680. · Zbl 0218.22004 · doi:10.1215/S0012-7094-57-02475-4
[6] Št. Schwarz: O maksimal’nych idealach v teorii polugrupp I, II. Czechoslovak Math. J. 3 (78) (1953), 139-153, 365-383.
[7] Št. Schwarz: Maximálne ideály a štruktúra pologrúp. Mat. fyz. časopis SAV 3 (1953), 17-39.
[8] Št. Schwarz: Subsemigroups of simple semigroups. Czechoslovak Math. J. 13 (88) (1963), 226-239. · Zbl 0122.02402
[9] O. Zariski P. Samuel: Commutative algebra, vol. I. Princeton, 1958. · Zbl 0081.26501
[10] R. Šulka: O nil’potentnych elementach, idealach i radikalach polugruppy. Mat. fyz. časopis SAV 13 (1963), 209-222.
[11] R. Fulp: Generalized semigroup kernels. Pacific J. Math. 24 (1968), 93 - 101. · Zbl 0165.03501 · doi:10.2140/pjm.1968.24.93
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